A Sparse $Z_2$ Chain Complex Without a Sparse Lift
Quantum Physics
2025-10-01 v2 Geometric Topology
Abstract
We construct a sparse chain complex (with three different degrees, so that it corresponds to a quantum code) which does not admit a sparse lift to the integers, answering a question in Ref. 1.
Cite
@article{arxiv.2509.22998,
title = {A Sparse $Z_2$ Chain Complex Without a Sparse Lift},
author = {Matthew B. Hastings},
journal= {arXiv preprint arXiv:2509.22998},
year = {2025}
}
Comments
6 pages, 0 figures; v2 minor typos